A conventional permanent magnet rotary electric machine is disclosed, for example, in Patent Literatures 1 and 2. The permanent magnet rotary electric machine includes a rotor placed in a hollow portion of a stator with an air gap between the rotor and the stator. A plurality of radial projections are provided on an outer periphery of a rotor core, and a thin permanent magnet is disposed between adjacent projections. A radial height of the projection is set to be less than a thickness of middle of the permanent magnet.